Design of a Discrete-time Output-feedback Based Repetitive-control System

Abstract

This paper deals with the problem of designing a robust discrete output-feedback based repetitive-control system for a class of linear plants with periodic uncertainties. The periodicity of the repetitive-control system is exploited to establish a two-dimensional (2D) model that converts the design problem into a robust stabilization problem for a discrete 2D system. By employing Lyapunov stability theory and the singular-value decomposition of the output matrix, a linear-matrix-inequality (LMI) based stability condition is derived. The condition can be used directly to design the gains of the repetitive controller. Two tuning parameters in the LMI enable the preferential adjustment of control and learning. A numerical example illustrates the design procedure and demonstrates the validity of the method.

Robust $$H_\infty $$ H ∞ Repetitive Control for a Class of Linear Stochastic Switched Systems with Time Delay

“…The stability criterion presented here is in the mean square sense, which is different from those stability results [28,33,[41][42][43]. Due to the existence of stochastic disturbance and time delay in system (20), the stochastic system theory and Lyapunov functional technique are utilized for the stability analysis.…”

“…Remark 2 Some previous results on H ∞ repetitive controller design of some dynamic systems can be found in [13,41,42]; however, these results cannot be directly applied to design the H ∞ repetitive controller for the system addressed in this paper because the factors of stochastic disturbance, switch, and time delay, which bring difficulties in the controller design, are not taken into account in these papers [13,41,42]. In this paper, the stochastic system theory and Lyapunov functional technique are used for the H ∞ repetitive controller design.…”

“…Based on the internal model principle, Inoue et al [14] added a human-like learning capability to a control system and devised a new control strategy called repetitive control [28,33,41]. Repetitive control is an efficient method to track or reject periodic exogenous signals.…”

State-Estimator-Based Asynchronous Repetitive Control of Discrete-Time Markovian Switching Systems

“…Based on the numerical simulations results, the asynchronous repetitive control method proposed in this paper has the following advantages over the methods provided in [32][33][34][35][36][37][38][39]: (1) the proposed method does not require the controller or estimator to switch synchronously with the plant; (2) the proposed asynchronous repetitive control method is broader and inclusive in the sense that a variety of more restrictive cases can be obtained from it. For example, when N � M and μ ip � 1 for p � i, i.e., μ � I, the asynchronous repetitive control method reduces to the synchronous mode-dependent case.…”

“…Since the control tasks in many applications that can be modeled by such systems are often repetitive, increased use of repetitive control formulations can be found in many applications, disk drive systems [28], rotating machinery [29], micro-/nanomanipulation applications [30], and power electronics systems [31]; repetitive control strategies use error measurements from the previous period to reduce subsequent steady-state tracking errors for periodic exogenous input signals. ere is a rich body of literature related to repetitive control design techniques [32][33][34][35][36][37][38][39][40]. Most repetitive control designs in the literature are developed for deterministic systems, whereas designs for switched stochastic dynamical systems are sparse.…”